Computing the optimal ate pairing over elliptic curves with embedding degrees 54 and 48 at the 256-bit security level
type: Item
instance of: scholarly article
title: Computing the optimal ate pairing over elliptic curves with embedding degrees 54 and 48 at the 256-bit security level
zbMATH Open document ID: 1461.94083
DOI: 10.1504/IJACT.2020.107167
author: Narcisse Bang Mbiang
author: Diego De Freitas Aranha
author: Emmanuel Fouotsa
published in: International Journal of Applied Cryptography
publication date: 2021-04-22T00:00:00Z
review text: Summary: Due to recent advances in the computation of finite fields discrete logarithms, the Barreto-Lynn-Scott family of elliptic curves of embedding degree 48 became suitable for instantiating pairing-based cryptography at the 256-bit security level. Observing the uncertainty around determining the constants that govern the best approach for computing discrete logarithms, \textit{M. Scott} and \textit{A. Guillevic} [Lect. Notes Comput. Sci. 11321, 43--57 (2018; Zbl 1446.11121)] consider pairing-friendly elliptic curves of embedding degree higher than 50, and discovered a new family of elliptic curves with embedding degree 54. This work aims at investigating the theoretical and practical cost of both the Miller algorithm and the final exponentiation in the computation of the optimal ate pairing on the two aforementioned curves. Both our theoretical results, based on the operation counts of base-field operations, and our experimental observations collected from a real implementation, confirm that BLS48 curves remain the faster curve in the computation of the optimal ate pairing at the 256-bit security level.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 7336558
zbMATH Keywords: elliptic curves
zbMATH Keywords: pairing-friendly curves
zbMATH Keywords: optimal pairings
zbMATH Keywords: Miller loop
zbMATH Keywords: final exponentiation
zbMATH Keywords: embedding degrees 48 and 54
zbMATH Keywords: 256 bits security level
MaRDI profile type: Publication
full work available at URL: ijact.2020.107167
OpenAlex ID: W3011736806
description: scientific article; zbMATH DE number 7336558